2.14. Multiplying MatricesProblemYou want to multiply a pair of twodimensional arrays. Mathematicians and engineers often need this. SolutionUse the PDL modules, available from CPAN. PDL is the Perl Data Language  modules that give fast access to compact matrix and mathematical functions: use PDL; # $a and $b are both pdl objects $c = $a * $b; Alternatively, apply the matrix multiplication algorithm to your twodimensional array: sub mmult { my ($m1,$m2) = @_; my ($m1rows,$m1cols) = matdim($m1); my ($m2rows,$m2cols) = matdim($m2); unless ($m1cols == $m2rows) { # raise exception die "IndexError: matrices don't match: $m1cols != $m2rows"; } my $result = []; my ($i, $j, $k); for $i (range($m1rows)) { for $j (range($m2cols)) { for $k (range($m1cols)) { $result>[$i][$j] += $m1>[$i][$k] * $m2>[$k][$j]; } } } return $result; } sub range { 0 .. ($_[0]  1) } sub veclen { my $ary_ref = $_[0]; my $type = ref $ary_ref; if ($type ne "ARRAY") { die "$type is bad array ref for $ary_ref" } return scalar(@$ary_ref); } sub matdim { my $matrix = $_[0]; my $rows = veclen($matrix); my $cols = veclen($matrix>[0]); return ($rows, $cols); } Discussion
If you have the PDL library installed, you can make use of its lightningfast manipulation of numbers. This requires far less memory and CPU than Perl's array manipulation. When using PDL objects, many numeric operators (such as use PDL; $a = pdl [ [ 3, 2, 3 ], [ 5, 9, 8 ], ]; $b = pdl [ [ 4, 7 ], [ 9, 3 ], [ 8, 1 ], ]; $c = $a x $b; # x overload If you don't have the PDL library, or don't feel like pulling it in for a small problem, you can always do the work yourself the good oldfashioned way. # mmult() and other subroutines as above $x = [ [ 3, 2, 3 ], [ 5, 9, 8 ], ]; $y = [ [ 4, 7 ], [ 9, 3 ], [ 8, 1 ], ]; $z = mmult($x, $y); 
